Find the derivative of the function.
-$$y = \frac { x ^ { 3 } } { x - 1 }$$
A) $y ^ { \prime } = \frac { 2 x ^ { 3 } - 3 x ^ { 2 } } { ( x - 1 ) ^ { 2 } }$
B) $y ^ { \prime } = \frac { - 2 x ^ { 3 } + 3 x ^ { 2 } } { ( x - 1 ) ^ { 2 } }$
C) $y ^ { \prime } = \frac { - 2 x ^ { 3 } - 3 x ^ { 2 } } { ( x - 1 ) ^ { 2 } }$
D) $y ^ { \prime } = \frac { 2 x ^ { 3 } + 3 x ^ { 2 } } { ( x - 1 ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

To find the derivative of $y = \frac{x^3}{x-1}$, we use the quotient rule: $(\frac{u}{v})' = \frac{u'v - uv'}{v^2}$. Let $u = x^3$ and $v = x - 1$. Then, $u' = 3x^2$ and $v' = 1$. Plugging these into the quotient rule formula gives $y' = \frac{(3x^2)(x-1) - (x^3)(1)}{(x-1)^2}$, which simplifies to $\frac{3x^3 - 3x^2 - x^3}{(x-1)^2} = \frac{2x^3 - 3x^2}{(x-1)^2}$.

Find the Derivative of the Function y=x3x−1y = \frac { x ^ { 3 } } { x - 1 }y=x−1x3​

Find the Derivative of the Function $y = \frac { x ^ { 3 } } { x - 1 }$